Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres
Abstract
Let Ω be a planar Jordan domain and α > 0. We consider double-dome-like surfaces Σ(Ω, t
α
) over
Ω where the height of the surface over any point x ∈ Ω equals dist(x, ∂Ω)
α
. We identify the necessary and
su cient conditions in terms of Ω and α so that these surfaces are quasisymmetric to S
2
and we show that
Σ(Ω, t
α
) is quasisymmetric to the unit sphere S
2
if and only if it is linearly locally connected and Ahlfors
2-regular.
Main Author
Format
Articles
Research article
Published
2016
Series
Subjects
Publication in research information system
Publisher
De Gruyter Open
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201603211907Use this for linking
Review status
Peer reviewed
ISSN
2299-3274
DOI
https://doi.org/10.1515/agms-2016-0002
Language
English
Published in
Analysis and Geometry in Metric Spaces
Citation
- Vellis, V. (2016). Weak Chord-Arc Curves and Double-Dome Quasisymmetric Spheres. Analysis and Geometry in Metric Spaces, 4(1). https://doi.org/10.1515/agms-2016-0002
License
Copyright© 2016 Vyron Vellis, published by De Gruyter Open.
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.